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Working with Probabilities Physics 115a (Slideshow 1) A. AlbrechtPowerPoint Presentation

Working with Probabilities Physics 115a (Slideshow 1) A. Albrecht

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Physics 115a (Slideshow 1)

A. Albrecht

These slides related to Griffiths section 1.3

Consider the following group of people in a room:

Total people = 14

Consider the following group of people in a room:

Total people = 14

Consider the following group of people in a room:

Total people = 14

Consider the following group of people in a room:

Total people = 14

Consider the following group of people in a room:

Total people = 14

Consider the following group of people in a room:

Total people = 14

Consider the following group of people in a room:

Total people = 14

NB: The probabilities for ages not listed are all zero

Total people = 14

Assuming Age<20, what is the probability of finding each age?

Total people = 14

Assuming Age<20, what is the probability of finding each age?

Total people = 14

Assuming Age<20, what is the probability of finding each age?

Total people = 14

Assuming no age constraint, what is the probability of finding each age?

Related to collapse of the waveunction (“changing the question”)

Total people = 14

Assuming Age<20, what is the probability of finding each age?

Related to collapse of the waveunction (“changing the question”)

Total people = 14

Consider a different room with different people: age?

Total people = 15

Consider a different room with different people: age?

Total people = 15

Red Room Numbers age?

Combine Red and Blue rooms age?

Total people = 29

- Lessons so far age?
- A simple application of probabilities
- Normalization
- “Re-Normalization” to answer a different question
- Adding two “systems”.
- All of the above are straightforward applications of intuition.

Expectation Values age?

Most probable answer = 25 age?

Median = 23

Average = 21

Lesson: Lots of different types of questions (some quite similar) with different answers. Details depend on the full probability distribution.

Average (mean): age?

- Standard QM notation
- Called “expectation value”
- NB in general (including the above) the “expectation value” need not even be possible outcome.

Careful: In general age?

In general, the average (or expectation value) of some function f(j) is

Continuous Variables age?

Continuous Variables age?

Why not measure age in weeks?

Blue room in weeks age?

Blue room in weeks age?

Another case where a measure of age in weeks might by useful:

The ages of students taking health in the 8th grade in a large school district (3000 students).

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